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Complexity analysis of primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term

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  • In this paper, we present a class of large- and small-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term. For both versions of the kernel-based interior-point methods, the worst case iteration bounds are established, namely, $O(n^{\frac{2}{3}}\log\frac{n}{\varepsilon})$ and $O(\sqrt{n}\log\frac{n}{\varepsilon})$, respectively. These results match the ones obtained in the linear optimization case.
    Mathematics Subject Classification: Primary: 90C05, 90C51; Secondary: 65K05.

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